Schwarzschild Radius of Masses Other Than Black Holes

[FanticalZappy]

Recently I have been researching black holes, and came across the "Schwarzschild Radius". The wikipedia page on Schwarzschild radius's mentioned that the Sun has a radius of 3km. If that is so, then how can that be so, as that would mean that light cannot escape it.

So when it said "3km", did they mean that the radius was 3km, or that the radius is 3km larger than that of the sun?

- James

Edit: This is my first post and I am not used to the way forums work, so if i have gotten something wrong then please excuse me.

 

[ShayanJ]

First, this is a subject under General Relativity not Quantum Mechanics.
Second, consider an object with mass m. It can have any shape. Schwarzschild Radius is the radius of a sphere that if that sphere with that radius had the mass m, then it would become a black hole. It is in fact the critical radius which means any radius smaller than Schwarzschild Radius has the same property.

 

[Nugatory]

So when it said "3km", did they mean that the radius was 3km, or that the radius is 3km larger than that of the sun?

It's neither.

The Schwatzchild radius is a quantity calculated from the mass of a spherically symmetric object. If the radius of the object is smaller than the Schwarzschild radius, it becomes a black hole with the event horizon at the Schwarzschild radius. However if (like the sun) the object is larger than its Schwarzschild radius, the Schwarzschild radius has no physical significance.

Thus, you can interpret the wikipedia article as saying that the sun isn't a black hole, but if it were, it would be only 6 km across.